Question

hii i've 2 eqns
(x-x1)^2+(y-y1)^2-d1^2=0
(x-x2)^2+(y-y2)^2-d2^2=0
these 2 eqns are need to be solved for x and y?

Answer 1

\[(x-x1)^{2}+(y-y1)^{2}+(d1)^{2}=0 ----(1)
(x-x1)^{2}+(y-y1)^{2}+(d1)^{2}=0----(2)\]

Answer 2

The equations as written in your question are the equations of two circles, the first for a circle of radius d1 with centre at (x1,y1) and the second with radius d2 and centre at (x2,y2). You can sketch some examples, and see some of the possibilities for intersections of the two circles. What I'm suggesting is a look at the geometry of the problem, for one view.

Turning to the algebra, you can expand each equation, and each one becomes x^2 + y^2 plus terms in x, y, and constants. Subtracting the two expanded equations, the x^2 and y^2 vanish, and you are left with something linear in x and y. The equation of a line. The solutions must lie on that line. Relate back to the geometric view. What is the slope of that line? Is it perpendicular to another line you can identify in the geometry?

Working back and forth between the geometric view and the algebraic representation, you can get some insight.

Finally, turning back to the algebra, if you have a linear relationship for x and y (the line equation), you can solve for y (or x), substitute that into one of the circle equations, and get a quadratic in x (or y). Then solve that quadratic to obtain two values of x (or y).

Hope that helps. Best wishes!

Answer 3

Thanks a lot for the info...